# In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0, if he opposed, and X = 1, if he is in favour. Find E(X) and Var (X).

$\begin{array}{1 1}E(X) = 0.7, V(X) = 0.21 \\E(X) = 0.7, V(X) = 0.49 \\ E(X) = 0.7, V(X) = 0 \\ E(X) = 0.7, V(X) = 0.14\end{array}$

Toolbox:
• Mean of the probability distribution = $\sum (X_i \times P(X_i))$ The Expected value of X is nothing but the mean of X.
• Standard Deviation = $\sqrt{\text{Variance}}$, where Variance $= E (X^2) - E(X)^2$
Given P (X = 0) = 30% = 0.3 and P (X = 1) = 70% = 0.7
Given this, the mean or $E (X) = 0 \times 0.3 + 1 \times 0.7 = 0.7$
$E (X^2) = 0^2 \times 0.3 + 1^2 \times 0.7 = 0.7$
Variance $= E(X^2) - E(X)^2) = 0.7 - 0.7^2 = 0.7 - 0.49 = 0.21$